The reduced expressions in a Coxeter system with a strictly complete Coxeter graph

Let (W,S)(W,S) be a Coxeter system with a strictly complete Coxeter graph. The present paper concerns the set Red(z)Red(z) of all reduced expressions for any z∈Wz∈W. By associating each bc-expression to a certain symbol, we describe the set Red(z)Red(z) and compute its cardinal |Red(z)||Red(z)| in terms of symbols. An explicit formula for |Red(z)||Red(z)| is deduced, where the Fibonacci numbers play a crucial role.